[EM] Condorcet Flavored PR Methods

[Forest Simmons]

Now I'll try to tackle the second question:

On Thu, 7 Nov 2002, Adam Tarr wrote in part:

> - I will admit this is the first election method I've dealt with where I
> have trouble manipulating small examples.  Here's a very small example that
> was giving me trouble: say we are electing two candidates out of four.
> My
> ballot is: A(>B=C=D).  The pairwise matrix will be 6x6 (with 6 empty
> slots).  With respect to my ballot, every comparison is equivalent to one
> of the following:
>
> AB vs. CD
> (k1 + j2 = 1 + 1 = 2?  k2 + j1 = 0 + .5 = .5?)
>
> or
>
> AB vs. BD
> (k1 + j2 = .5 + 1 = 1.5?  k2 + j1 = 0 + 1 = 1?)

On this one I get M=A and m=D, so k1=.5, k2=0, and j2=.5+.5=1, as you have
noted, but I get j1=.5, since B=D=m, instead of the j1=1 that you got.


>
> or
>
> AB vs. AC
>
> (k1 + j2 = k2 + j1 = 1.5 + .5 = 2)
>
> Do the summations I wrote make sense?  The results (except the trivial last
> one) seem a bit odd.  I was toying with this example to try and measure how
> equivalent your Condorcet-PR method is to PAV in situations where the
> voters vote in an approval-like fashion.


It does seem odd that AB should beat CD by a larger margin than AB's win
over BD when B and D are ranked equally.

Perhaps we should interpret the difference AB-CD as just A when B is equal
in rank to a member of CD.

In other words, if we have two sets H and K, then we should interpret H-K
as consisting of those members of H that are not equivalent to any member
of K.

[Two candidates are "equivalent" on a ballot if they have equal rank.]

If we do this, then AB beats CD by the same margin as in the AB vs. BD
contest, which makes more sense.

Thanks for pointing that out.

Forest

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